In this paper we consider the finite deformation of a magnetized and/or polarized elastic body, placed in an electro-magnetic field. We shall be concerned with the general dynamic problem, in which the body may be magnetically saturated or non-saturated, and may conduct currents. But we shall confine our considerations to the non-relativistic case, i.e. we assume the velocities to be small with respect to the velocity of light. In our theory we aim at a unification of electro-magnetic theory and continuum mechanics: we shall derive the force distribution of electro-magnetic origin and the influence of the deformation of the body on the field.